In a large stock pot with boiling water cook lobsters for 2 minutes. Remove from water and immediately plunge into an ice bath. When lobsters are fully cooled, remove from ice bath. With a large knife split lobsters in half lengthwise. Clean lobsters and refrigerate until ready to grill.
Preheat the grill. Spoon garlic butter over cut side of lobsters. Place cut side up on grill and cook for about 8 to 10 minutes or until lobster meat is cooked. Finish each lobster with some sauce verte and a slice of lemon to the side. Serve immediately.
In a small pot, combine butter with garlic and lemon juice. On a low heat melt butter and keep warm.
In a small mixing bowl, whisk oil, vinegar and mustard together. Add all other ingredients and refrigerate until ready to use.